How to ignore HTML element from tabindex?

Don't forget that, even though tabindex is all lowercase in the specs and in the HTML, in Javascript/the DOM that property is called tabIndex.

Don't lose your mind trying to figure out why your programmatically altered tab indices calling element.tabindex = -1 isn't working. Use element.tabIndex = -1.

If these are elements naturally in the tab order like buttons and anchors, removing them from the tab order with tabindex="-1" is kind of an accessibility smell. If they're providing duplicate functionality removing them from the tab order is ok, and consider adding aria-hidden="true" to these elements so assistive technologies will ignore them.

You can use tabindex="-1".

Only do this if you are certain it does not remove functionality for keyboard users.

The W3C HTML5 specification supports negative tabindex values:

If the value is a negative integer
The user agent must set the element's tabindex focus flag, but should not allow the element to be reached using sequential focus navigation.

Watch out though that this is a HTML5 feature and might not work with old browsers.
To be W3C HTML 4.01 standard (from 1999) compliant, tabindex would need to be positive.

Sample usage below in pure HTML.

<a href="#" onclick="return false">Focusable</a>
<a tabindex="-1" href="#" onclick="return false">Not focusable</a>
<a href="#" onclick="return false">Focusable</a>